The map \(\mathsf {k}\)  is closely related with map (2.17) in [1]} given by \(\mathsf {i} \, : \, \mathrm {T} M \otimes \mathrm {T}^* M \longrightarrow \Lambda ^3 T^* M \) ,
\(a = \textstyle \sum _{i,j \in \mathrm {Z}_7} a_{i\, j} e_i \otimes e_j^* \longrightarrow \mathsf {i}(a) = \sum _{i,j \in \mathrm {Z}_7} a_{i\, i} e_i^*\wedge (e_j \varphi )\) 
